dolution

Three middle schools in Raleigh, NC can each accommodate 1200 students. To make it easy to provide transportation to all school kids, the Wake County Schools has segmented the area into 5 distinct territories: (1) North (2) South (3) East (4) West (5) Central—each with different high school student populations. Centralia School, WestHall School and Southside School are situated in the central, west, and south territories. In certain instances, students must be picked up from outside their respective territories. James the School Administrator seeks minimize the total distance that the students have to travel. The distances in miles from each territory to the three schools and the total student populations are shown below:

As a Linear Programming whiz, you have been tasked by James to analyze this situation and help him figure out how many school kids to bus from each territory to minimize the total miles traveled.

a) Formulate a linear programming model for this problem.

b) Solve the model by using the computer.

c) If James decided that because all students in the north and east districts must be picked up by bus, then at least 50% of the students who live in the south, west, and central districts must also be bused to another district. Reformulate the linear programming model to reflect this new set of constraints and solve by using the computer.

d) James has further decided that the enrollment at all three schools should be equal. Formulate this additional restriction in the linear programming model and solve by using the computer.